I was thinking about structural differences between a marriage between two parties and an arrangement with more than two parties. Here are two structural differences.
1. Once you have three persons, you have politics, and not just a relationship. You can have alliances.
2. If you are married to one person, a conflict solely about the apportionment of goods between you and the other person can be resolved by your sacrificing your own good. But if there are three or more persons in the marriage, your self-sacrifice won't solve all such problems, because some goods-apportionment conflicts between the people in the marriage will concern goods to parties other than yourself, rather than between your goods and that of another.